To find the area of a triangle given its vertices $A(0, 0)$, $B(3, 8)$, and $C(9, 0)$, we can use the formula for the area of a triangle based on its vertices:

$\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|$

where:

• $A(x_1, y_1)$,
• $B(x_2, y_2)$,
• $C(x_3, y_3)$.

Plugging in the coordinates $A(0, 0)$, $B(3, 8)$, and $C(9, 0)$:

$\text{Area} = \frac{1}{2} \left| 0(8 - 0) + 3(0 - 0) + 9(0 - 8) \right|$ $\text{Area} = \frac{1}{2} \left| 0 + 0 + 9(-8) \right|$ $\text{Area} = \frac{1}{2} \left| -72 \right|$ $\text{Area} = \frac{1}{2} \times 72 = 36$

So, the area of the triangle is $36 \, \text{square units}$.

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Would you like a more detailed explanation? Let me know if you have any questions!

Here are some related questions for you:

1. How does the area formula for a triangle with vertices come about?
2. What happens if one of the points of the triangle is at the origin (0, 0)?
3. How would you find the area of a triangle given the lengths of its sides instead of coordinates?
4. Can you use this formula for triangles in 3D space? How would it change?
5. What is the relationship between the base and height of a triangle and its area?

Tip: Always double-check the coordinates to ensure you're using the correct points before applying the formula.